Library / Vibration exposure / VIB-10
Vibration exposure
Time to reach a chosen exposure value
Time at a constant weighted level before the daily exposure reaches a chosen target such as an action or limit value.
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- VIB-10
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- v1
- Field
- Vibration exposure
- Result
- T [h]
For a constant weighted RMS aw on a given axis with axis multiplier k, and no previous daily dose, A(8) reaches a chosen value Atarget after T = T0(Atarget/(k aw))² with T0 = 8 h. Time appears under a square root in A(8), so halving the level allows four times as long. Keep the axis multiplier in the expression unless the acceleration has already been multiplied by it. Take the shortest time across the axes that have a non-zero ongoing exposure.
Time at a constant weighted level before the daily exposure reaches a chosen target such as an action or limit value. Because time enters as a square root, halving the level allows four times as long.
Calculator
- Time to the action value 0.5 m/s²1.653 h
- Time to the limit value 1.15 m/s²8.744 h
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At a z-axis level of 1.1 m/s² the daily exposure reaches 0.5 m/s² after 1.653 h. For the limit value of 1.15 m/s² it takes 8.744 h; the lecture’s own values are 1.653 h and 8.744 h.
- Halving the level to 0.55 m/s² would allow 6.612 h, four times as long, which is why reducing the level by speed limits or a better seat is so effective.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (h) | Local step | Change in result |
|---|---|---|---|---|---|---|
| aw Weighted RMS acceleration | 0.1 to 3 m/s² | 0.2222 | 200 | 199.8 | +10% | −17.4 % |
| Atarget Target daily exposure | 0.2 to 1.5 m/s² | 0.2645 | 14.88 | 14.61 | +10% | +21 % |
| k Axis multiplier | 1 to 1.4 | 0.8433 | 1.653 | 0.8096 | +10% | −17.4 % |
Sweep of Weighted RMS acceleration
| Weighted RMS acceleration (m/s²) | Time to reach the target (h) |
|---|---|
| 0.1 | 200 |
| 0.4625 | 9.35 |
| 0.825 | 2.938 |
| 1.188 | 1.418 |
| 1.55 | 0.8325 |
| 1.913 | 0.5468 |
| 2.275 | 0.3864 |
| 2.638 | 0.2875 |
| 3 | 0.2222 |
Sweep one variable
Variables and how each one contributes
Time to reach the target
What the equation gives you. Everything else feeds it.
Target daily exposure
The target daily exposure value, in m/s²: for example the UK action value 0.5 or limit value 1.15. Raises the time with the square of the target. Raising it by 10 % (to 0.55) moves the result by +21 %, from 1.653 to 2 h.
Axis multiplier
The axis multiplier: 1.4 for x and y, 1.0 for z. Lowers the time with the square of the multiplier. Raising it by 0.1 (to 1.1) moves the result by −17.4 %, from 1.653 to 1.366 h.
Weighted RMS acceleration
The weighted RMS acceleration on the axis, in m/s². Lowers the time with the square of the level: a 10 % rise gives about 17 % less time. Raising it by 10 % (to 1.21) moves the result by −17.4 %, from 1.653 to 1.366 h.
Worked example with the values above
- Ratio of target to multiplied level: Atarget/(k aw) = 0.5/(1 × 1.1) = 0.4545.
- Square it and multiply by 8 h: 0.2066 × 8.
- T = 1.653 h.
Assumptions and limits
- A constant weighted RMS on one axis, with no earlier exposure that day.
- The exposure is measured against a chosen A(8) target; these are arithmetic times, not guaranteed symptom-free operating times.
Common mistakes
- Dropping the axis multiplier from the denominator.
- Using the result as a guaranteed safe working time.
Statistics and uncertainty
Because the time depends on the square of the level, a ±10 % error in the weighted RMS gives about ±20 % in the allowed time. Treat times near a limit as uncertain by that much.
Where it is used
- Setting a driving-time limit for a vehicle or route with a measured vibration level.
- Comparing how long different vehicles can be driven before the action value is reached.
Maths you need
- Daily exposure A(8): normalised to eight hours
- Squares and square roots: time enters as a square